Echo control is an important problem in telecommunication systems. In public switched telephony networks (PSTN), echo is sometimes generated in the four to two wire connections because of impedance mismatch. More precisely, the local loops between the subscriber and the switch use two wire connections, while the connections between switches use four wires. The coupling between two wire and four wire connections is performed with an electrical device called a hybrid. Ideally, the hybrid should direct all incoming signal energy from the far end (the distant speaker) to the near end terminal. Since the connection is a duplex connection it must be possible for the near end speaker to talk also when the far end speaker is talking. Unfortunately, this means that some signal energy coming from the far end can be reflected back to the far end because of impedance mismatch in the hybrid. These hybrids are numerous, and hence it is not feasible to tune them manually. The situation is symmetrical, i.e. the same effects occur at the far end when the near end is speaking.
In an attempt to solve the echo cancellation problem it has been suggested to use adaptive filters, especially filters that are updated in accordance with the NLMS algorithm. This algorithm is attractive due to its relatively low complexity. However, a drawback of the algorithm is its slow convergence.